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nika2105 [10]
3 years ago
12

According to the rational root theorem what are all the potential rational roots of f(x)=9x^4-2x^2-3x+4

Mathematics
1 answer:
8_murik_8 [283]3 years ago
7 0

Answer:

+/- 1, \frac{+-1}{+-3},\frac{+-1}{+-9},+-2,\frac{+-2}{+-3},\frac{+-2}{+-9},+-4,\frac{+-4}{+-3}, \frac{+-4}{+-9} ....

Step-by-step explanation:

The Rational root theorem states that If f(x) is a Polynomial with integer coefficients and if there exist a rational root of the form p/q then p is the factor of the constant term of the function and q is the factor of the  leading coefficient of the function

Given: f(x)= 9x^4-2x^2-3x+4

Factors of q (leading coefficient) are: +/-9, +/-3, +/-1

Factors of p (constant term) are: +/-4 , +/-2, +/- 1

According to the theorem we write the roots in p/q form:

Therefore,

p/q =+/- 1, \frac{+-1}{+-3},\frac{+-1}{+-9},+-2,\frac{+-2}{+-3},\frac{+-2}{+-9},+-4,\frac{+-4}{+-3}, \frac{+-4}{+-9} ....

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A man is hiking in Death Valley. He starts at an elevation of 65 feet above sea level and descends to an elevation 30 feet below
kati45 [8]

Answer:

95 feet

Step-by-step explanation:

In Death Valley, hiking man starts at 65 feet above sea level and then descends 30 feet below sea level. The man needs 65 feed to reach sea level, then from there he travels 30 feet more.

Thus he travels the sum of this distances, i.e 65+30 = 95 feet

5 0
3 years ago
Ann has 30 jobs that she must do in sequence, with the times required to do each of these jobs being independent random variable
IgorLugansk [536]

Answer:

P(T_A < T_B) = P(T_A -T_B

Step-by-step explanation:

Assuming this problem: "Ann has 30 jobs that she must do in sequence, with the times required to do each of these jobs being independent random variables with mean 50 minutes and standard deviation 10 minutes. Bob has 30 jobs that he must do in sequence, with the times required to do each of these jobs being independent random variables with mean 52 minutes and standard deviation 15 minutes. Ann's and Bob's times are independent. Find the approximate probability that Ann finishes her jobs before Bob finishes his jobs".

Previous concepts

The central limit theorem states that "if we have a population with mean μ and standard deviation σ and take sufficiently large random samples from the population with replacement, then the distribution of the sample means will be approximately normally distributed. This will hold true regardless of whether the source population is normal or skewed, provided the sample size is sufficiently large".

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

Solution to the problem

For this case we can create some notation.

Let A the values for Ann we know that n1 = 30 jobs solved in sequence and we can assume that the random variable X_i the time in order to do the ith job for i=1,2,....,n_1. We will have the following parameters for A.

\mu_A = 50, \sigma_A =10

W can assume that B represent Bob we know that n2 = 30 jobs solved in sequence and we can assume that the random variable [tex[X_i[/tex] the time in order to do the ith job for i=1,2,....,n_2. We will have the following parameters for A

\mu_B = 52, \sigma_B =15

And we can find the distribution for the total, if we remember the definition of mean we have:

\bar X= \frac{\sum_{i=1}^n X_i}{n}

And T =n \bar X

And the E(T) = n \mu

Var(T) = n^2 \frac{\sigma^2}{n}=n\sigma^2

So then we have:

E(T_A)=30*50 =1500 , Var(T_A) = 30*10^2 =3000

E(T_B)=30*52 =1560 , Var(T_B) = 30 *15^2 =6750

Since we want this probability "Find the approximate probability that Ann finishes her jobs before Bob finishes his jobs" we can express like this:

P(T_A < T_B) = P(T_A -T_B

Since we have independence (condition given by the problem) we can find the parameters for the random variable T_A -T_B

E[T_A -T_B] = E(T_A) -E(T_B)=1500-1560=-60

Var[T_A -T_B]= Var(T_A)+Var(T_B) =3000+6750=9750

And now we can find the probability like this:

P(T_A < T_B) = P(T_A -T_B

P(\frac{(T_A -T_B)-(-60)}{\sqrt{9750}}< \frac{60}{\sqrt{9750}})

P(Z

7 0
3 years ago
Which statement describes the inverse of m(x) = x2 – 17x?
Finger [1]

Answer:

The correct option is;

The \ domain \ restriction \ x \geq \dfrac{17}{2} \ results \ in \ m^{-1}(x) = \dfrac{17}{2} \pm \sqrt{x + \dfrac{289}{4} }}

Step-by-step explanation:

The given information is that m(x) = x² - 17·x

The above equation can be written in the form;

y = x² - 17·x

Therefore;

0 = x² - 17·x - y

From the general solution of a quadratic equation, 0 = a·x² + b·x + c we have;

x = \dfrac{-b\pm \sqrt{b^{2}-4\cdot a\cdot c}}{2\cdot a}

By comparison to the equation,0 = x² - 17·x - y, we have;

a = 1, b = -17, and c = -y

Substituting the values of a, b and c into the formula for the general solution of a quadratic equation, we have;

x = \dfrac{-(-17)\pm \sqrt{(-17)^{2}-4\times (1) \times (-y)}}{2\times (1)} = \dfrac{17\pm \sqrt{289+4\cdot y}}{2}

Which can be simplified as follows;

x =  \dfrac{17\pm \sqrt{289+4\cdot y}}{2}= \dfrac{17}{2} \pm \dfrac{1}{2}  \times \sqrt{289+4\cdot y}} = \dfrac{17}{2} \pm \sqrt{\dfrac{289}{4} +\dfrac{4\cdot y}{4} }}

And further simplified as follows;

x = \dfrac{17}{2} \pm \sqrt{\dfrac{289}{4} +y }} = \dfrac{17}{2} \pm \sqrt{y + \dfrac{289}{4} }}

Interchanging x and y in the function of the inverse, m⁻¹(x), we have;

m^{-1}(x) = \dfrac{17}{2} \pm \sqrt{x + \dfrac{289}{4} }}

We note that the maximum or minimum point of the function, m(x) = x² - 17·x found by differentiating the function and equating the result to zero, gives;

m'(x) = 2·x - 17 = 0

x = 17/2

Similarly, the second derivative is taken to determine if the given point is a maximum or minimum point as follows;

m''(x) = 2 > 0, therefore, the point is a minimum point on the graph

Therefore, as x increases past the minimum point of 17/2, m⁻¹(x) increases to give;

The \ domain \ restriction \ x \geq \dfrac{17}{2} \ results \ in \ m^{-1}(x) = \dfrac{17}{2} \pm \sqrt{x + \dfrac{289}{4} }} to increase m⁻¹(x) above the minimum.

8 0
2 years ago
Find the value of x in each triangle with the given angle measures.
Nataliya [291]

Answer:

15°

Step-by-step explanation:

Total degrees of a triangle is 180°

Angle 1: ?

Angle 2: 81°

Angle 3: 84°

180°- 81°- 84° = 15°

4 0
2 years ago
How do you find the product of (q 5)(5q-1)?
aksik [14]
Go to mathpapa.com 25q^(2)-5q
5 0
3 years ago
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